And what you want to do is
have the black parts as positive relief on the surface of a cylinder.
Note also that the background is not entirely white, it is light gray.

When you bring in the image
to PhotoToMesh you'll need increase the contrast and brightness a tad
to get the background to be white. You do this in the image import wizard:

Simply setting contrast and
brightness to 2 the background changes from light gray to white.

Now, since we want the dark
parts to be high in the relief we need to check Invert Mesh as shown in
step 1) below:

If we left it at that we would
get the black parts being raised, but the white parts, the surrounding
rectangle, would be lowered into the body of the cylinder:

The "background"
is the object's surface everywhere except where your image is. Luckily
you can tell PhotoToMesh to assume that outside of the photo area the
background should be considered white. That is step 3 in the vignette
dialog as shown here:

And the result is shown here:

By putting Background Greyscale
to 100% we are saying "all areas outside the image are to be considered
white" which means that the white of the image, around the dark pattern,
blends in smoothly.